Meervoudig regressiemodel

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Tue, 07 Dec 2010 11:41:40 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/07/t12917220595ubikz28eewf2fx.htm/, Retrieved Tue, 07 Dec 2010 12:40:59 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/07/t12917220595ubikz28eewf2fx.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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User-defined keywords:

Dataseries X:

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16198,9 16896,2 0 16554,2 16698 0 19554,2 19691,6 0 15903,8 15930,7 0 18003,8 17444,6 0 18329,6 17699,4 0 16260,7 15189,8 0 14851,9 15672,7 0 18174,1 17180,8 0 18406,6 17664,9 0 18466,5 17862,9 0 16016,5 16162,3 0 17428,5 17463,6 0 17167,2 16772,1 0 19630 19106,9 0 17183,6 16721,3 0 18344,7 18161,3 0 19301,4 18509,9 0 18147,5 17802,7 0 16192,9 16409,9 0 18374,4 17967,7 0 20515,2 20286,6 0 18957,2 19537,3 0 16471,5 18021,9 0 18746,8 20194,3 0 19009,5 19049,6 0 19211,2 20244,7 0 20547,7 21473,3 0 19325,8 19673,6 0 20605,5 21053,2 0 20056,9 20159,5 0 16141,4 18203,6 0 20359,8 21289,5 0 19711,6 20432,3 1 15638,6 17180,4 1 14384,5 15816,8 1 13855,6 15071,8 1 14308,3 14521,1 1 15290,6 15668,8 1 14423,8 14346,9 1 13779,7 13881 1 15686,3 15465,9 1 14733,8 14238,2 1 12522,5 13557,7 1 16189,4 16127,6 1 16059,1 16793,9 1 16007,1 16014 1 15806,8 16867,9 1 15160 16014,6 0 15692,1 15878,6 0 18908,9 18664,9 0 16969,9 17962,5 0 16997,5 17332,7 0 19858,9 19542,1 0 17681,2 etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Uitvoer[t] = + 3664.99536024364 + 0.758111799349518Invoer[t] -755.194173669825Crisis[t] + 21.5710959597444M1[t] + 712.153992678052M2[t] + 1108.98645761485M3[t] + 658.062497580011M4[t] + 943.435882803938M5[t] + 1543.21131640386M6[t] + 1336.55397969346M7[t] -396.939668264646M8[t] + 1307.00770491500M9[t] + 1409.14358383855M10[t] + 881.69742401456M11[t] -9.70329327631562t + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 3664.99536024364 797.543088 4.5954 4.3e-05 2.1e-05 Invoer 0.758111799349518 0.043388 17.4727 0 0 Crisis -755.194173669825 204.573962 -3.6915 0.000665 0.000332 M1 21.5710959597444 284.60683 0.0758 0.939962 0.469981 M2 712.153992678052 287.242631 2.4793 0.017478 0.008739 M3 1108.98645761485 288.252772 3.8473 0.00042 0.00021 M4 658.062497580011 284.806008 2.3106 0.026096 0.013048 M5 943.435882803938 285.08977 3.3093 0.001987 0.000993 M6 1543.21131640386 287.199816 5.3733 4e-06 2e-06 M7 1336.55397969346 287.302675 4.6521 3.6e-05 1.8e-05 M8 -396.939668264646 304.79381 -1.3023 0.200255 0.100128 M9 1307.00770491500 300.051546 4.3559 9e-05 4.5e-05 M10 1409.14358383855 310.613321 4.5366 5.1e-05 2.6e-05 M11 881.69742401456 299.413557 2.9447 0.005363 0.002682 t -9.70329327631562 4.310699 -2.251 0.029951 0.014976 Multiple Linear Regression - Regression Statistics Multiple R 0.983895994867436 R-squared 0.96805132871618 Adjusted R-squared 0.956869293766844 F-TEST (value) 86.5720178037536 F-TEST (DF numerator) 14 F-TEST (DF denominator) 40 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 419.317970863194 Sum Squared Residuals 7033102.42755304 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 16198.9 16486.0717470964 -287.171747096376 2 16554.2 17016.6935919073 -462.493591907306 3 19554.2 19673.3062461005 -119.106246100505 4 15903.8 16361.4963266158 -457.696326615751 5 18003.8 17784.8718715986 218.928128401405 6 18329.6 18568.1108983965 -238.510898396461 7 16260.7 16449.1928967622 -188.492896762197 8 14851.9 15072.0881434337 -220.188143433656 9 18174.1 17909.640627936 264.459372064009 10 18406.6 18369.0751356483 37.5248643516694 11 18466.5 17982.0318188192 484.468181180771 12 16016.5 15801.3861755546 215.113824445439 13 17428.5 16799.7848627315 628.715137268482 14 17167.2 16956.4301569233 210.769843076683 15 19630 19113.5987577051 516.401242294942 16 17183.6 16844.4199958657 339.180004134308 17 18344.7 18211.7710788766 132.928921123394 18 19301.4 19066.1209924535 235.279007546545 19 18147.5 18313.6236979668 -166.123697966766 20 16192.9 15514.5286425983 678.371357401667 21 18374.4 18389.7592835283 -15.3592835283375 22 20515.2 20240.1773206872 275.022679312829 23 18957.2 19134.9746963343 -177.774696334272 24 16471.5 17094.7313583091 -623.23135830914 25 18746.8 18753.5212338995 -6.72123389945978 26 19009.5 18566.5902606261 442.909739373942 27 19211.2 19859.7388436892 -648.538843689151 28 20547.7 20330.5277470588 217.172252941189 29 19325.8 19241.8240337171 83.975966282904 30 20605.5 20877.7872124233 -272.287212423297 31 20056.9 19983.9020673579 72.9979326420792 32 16141.4 16757.9142577758 -616.514257775773 33 20359.8 20791.6155392918 -431.815539291780 34 19711.6 19479.0005168668 232.599483133214 35 15638.6 16476.5473034618 -837.947303461783 36 14384.5 14551.3853365779 -166.885336577904 37 13855.6 13998.4598487459 -142.859848745941 38 14308.3 14261.8472842862 46.4527157138439 39 15290.6 15519.0613680601 -228.461368060079 40 14423.8 14056.2861271888 367.513872811203 41 13779.7 13978.7519318195 -199.051931819466 42 15686.3 15770.3554629321 -84.0554629321237 43 14733.8 14623.260976884 110.539023115989 44 12522.5 12364.1689561922 158.331043807763 45 16189.4 16006.6845492439 182.715450756109 46 16059.1 16604.2470267977 -545.147026797712 47 16007.1 15475.8461813847 531.253818615283 48 15806.8 15231.7971295584 575.002870441603 49 15160 15351.9623075267 -191.962307526705 50 15692.1 15929.7387062572 -237.638706257163 51 18908.9 18429.1947844452 479.705215554793 52 16969.9 17436.0698032710 -466.169803270949 53 16997.5 17234.2810839882 -236.781083988236 54 19858.9 19499.3254337947 359.574566205337 55 17681.2 17510.1203610291 171.079638970895 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.295082536029619 0.590165072059238 0.704917463970381 19 0.157557984069704 0.315115968139407 0.842442015930296 20 0.155081102443636 0.310162204887272 0.844918897556364 21 0.256960791574247 0.513921583148494 0.743039208425753 22 0.254223546898218 0.508447093796437 0.745776453101782 23 0.447228224732796 0.894456449465592 0.552771775267204 24 0.547566420102008 0.904867159795983 0.452433579897992 25 0.432920223010381 0.865840446020762 0.567079776989619 26 0.50647254150704 0.98705491698592 0.49352745849296 27 0.758145005951734 0.483709988096533 0.241854994048266 28 0.705164731732354 0.589670536535292 0.294835268267646 29 0.706696578313557 0.586606843372886 0.293303421686443 30 0.61884814777722 0.76230370444556 0.38115185222278 31 0.555410642595643 0.889178714808713 0.444589357404357 32 0.540763424406889 0.918473151186223 0.459236575593112 33 0.444200163565878 0.888400327131756 0.555799836434122 34 0.648289080717038 0.703421838565923 0.351710919282962 35 0.64096043239817 0.71807913520366 0.35903956760183 36 0.494015290538161 0.988030581076321 0.505984709461839 37 0.326574089116922 0.653148178233845 0.673425910883078 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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